Engineers Want to Know What Factors Are Associated with Gas $\mathrm { MPG }$

Engineers want to know what factors are associated with gas mileage. The regression
below predicts the average miles per gallon (MPG) for 82 cars using their engine
horsepower (HP) and weight (WT, in 100's of pounds). Dependent variable is $\mathrm { MPG }$
R squared $= 82.4 \% \quad$ R squared (adjusted) $= 81.9 \%$
$\mathrm { s } = 4.255$ with $82 - 3 = 79$ degrees of freedom
\begin{tabular} { l c l c c }
\multicolumn{1}{c} { Source } & Sum of Squares & df & Mean Square & Fratio \\
Regression & $6676.84$ & 2 & $3338.42$ & 184 \\
Residual & $1430.62$ & 79 & $18.1091$ &
\end{tabular}
$\begin{array} { l l l l r } \text { Variable } & \text { Coefficient } & \text { SE(Coeff) } & \text { t-ratio } & \text { p-value } \\ \text { Constant } & 66.855 & 2.079 & 32.2 & < 0.0001 \\ \text { HP } & - 0.0209708 & 0.015 & - 1.4 & 0.1661 \\ \text { WT } & - 0.990369 & 0.1047 & - 9.45 & < 0.0001 \end{array}$
a. Write down the regression equation.
b. Write down the hypotheses for the test of the coefficient of horsepower. Conduct the test
and explain your conclusion in the context of this problem.
c. Write down the hypotheses for the test of the coefficient of weight. Conduct the test and
explain your conclusion in the context of this problem.
d. Explain the meaning of the coefficient of weight in the context of this problem.
e. Explain the meaning of the intercept of this regression in the context of this problem.
f. Compute the predicted gas mileage of a 3500 pound car with a 150 horsepower engine.
The plots are MPG vs. HP, MPG vs. WT, residuals vs. predicted values, and a normal
probability plot of residuals.
g. Check the conditions of this regression and comment on whether they are satisfied.